Question

State of Economy	Probability of State of Economy	Asset A Rate of Return	Asset B Rate of Return
Boom	0.1	0.25	0.08
Normal	0.4	0.15	0.03
Recession	0.5	-0.08	-0.01

Question 3 (1 point)

What is the standard deviation for asset A?

Question 3 options:

Question 4 (1 point)

What is the standard deviation for asset B?

Question 4 options:

Question 5 (1 point)

What is the expected return of a portfolio that has 80% in Asset A and 20% in Asset B?

Question 5 options:

Question 6 (1 point)

The standard deviation of the 80% A and 20% B portfolio most likely should

Question 6 options:

	A) Equal 80% X A's standard deviation plus 20% x B's standard deviation.
	B) Be greater than 80% X A's standard deviation plus 20% x B's standard deviation.
	C) Be less than 80% X A's standard deviation plus 20% x B's standard deviation.

Answer 1

Solution:

State of the Economy	Probability	Return on stock A(%)	Return on stock B(%)
Recession	0.1	0.25	0.08
Normal	0.4	0.15	0.03
Boom	0.5	-0.08	-0.01

Part A)

Expected return = ∑ probability * return

Expected Return A = .1 * 0.25 +0.4*0.15 +0.5*-0.08 = 0.045

Variance = ∑ probability * (return – expected return) ^2

Variance of A = .1 * (0.25-0.045) ^2 + .4 * (0.15-0.045) ^ 2 + .5 * (-0.08-0.045) ^2

                        = .1 * (0.2050) ^2 + .4 * (0.1050) ^ 2 + .5 * (-0.1250) ^2

                        = 0.006868

Standard Deviation = Sqrt of variance = 0.006868^(1/2) =  0.08287

Part B )

Expected Return B =.1 * 0.08 +0.4*0.03+0.5*-0.01 =0.015

Variance of B = .1 * (0.08-0.015) ^2 + .4 * (0.03- 0.015) ^ 2 + .5 * (-0.01- 0.015) ^2

                        = .1 * (0.065) ^2 + .4 * (0.015) ^ 2 + .5 * (-0.025) ^2

                        = 0.0005075

Standard Deviation = Sqrt of variance = 0.0005075^(1/2) =  0.02253

                        

Part C)

Expected return = E(R) = w1R1 + w2R2 (w1 and w2 are respective weights of asset in portfolio)

                               = 80% * 0.045 + 20% * 0.015 = 0.039 = 3.90%

  = 3.90 %

Part D )

State of the Economy	Probability	Return on stock A(%)	Return on stock B(%)	Return of Portfolio with Weight
Recession	0.1	0.25	0.08	=0.8*0.25+0.2*0.08= 0.216
Normal	0.4	0.15	0.03	0.126
Boom	0.5	-0.08	-0.01	-0.066

Expected return = 3.90%

Variance = ∑ probability * (return – expected return) ^2

= .1 * (0.216-0.039) ^2 + .4 * (0.126-0.039) ^ 2 + .5 * (-0.066-0.039) ^2

=0.011673

Standard Deviation = Sqrt of 0.011673 = 0.1080

This is more than the 80% of standard deviation of A + 20% of standard deviation B

Option B is correct